Lecture 41. Direct Sums of Vector Spaces
Автор: Yuly Billig
Загружено: 2024-03-07
Просмотров: 549
Описание:
0:00 Direct sum U⊕W of two vector spaces
3:19 Examples of direct sums
5:59 The summands are subspaces in the direct sum
8:06 Basis of a direct sum
15:23 dim(U⊕W) = dim U + dim W
16:07 Internal direct sum
20:34 Examples of decompositions of spaces into a direct sum of subspaces
26:44 Direct sum of eigenspaces for a diagonalizable operator
31:38 Special case: decomposing into a direct sum of two subspaces
34:25 Example: Decomposing matrices into symmetric and skew-symmetric matrices
39:42 Bases and dimensions of internal direct sums
In this lecture, we discuss external and internal direct sums of vector spaces.
This is a lecture in the "Linear Algebra" course for students specializing in mathematics.
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